LMFDB - Embedded newform 90.16.c.e.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,16,Mod(19,90)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 16, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("90.19");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 90 = 2 \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	90.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$128.424154590$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1960198978 x^{14} + \cdots + 25\!\cdots\!00 $ x^16 + 1960198978x^14 + 1419072122452249599x^12 + 475511948368963765554364384x^10 + 78505143006386219920881563766722959x^8 + 6306932914279579973235286083160651948918938x^6 + 243655669397438624319289580389876593903711764861841x^4 + 4141418827690700793980368732720094517394846053064084563300*x^2 + 25064779091755865960773413038603064397578710236940210149877760000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{94}\cdot 3^{32}\cdot 5^{18} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Root			$25766.7i$ of defining polynomial
Character	$\chi$	$=$	90.19
Dual form			90.16.c.e.19.11

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-128.000i q^{2} -16384.0 q^{4} +(-101852. + 141929. i) q^{5} -859408. i q^{7} +2.09715e6i q^{8} +(1.81669e7 + 1.30370e7i) q^{10} +2.70335e7 q^{11} +3.33134e8i q^{13} -1.10004e8 q^{14} +2.68435e8 q^{16} +1.06804e9i q^{17} -2.29839e9 q^{19} +(1.66874e9 - 2.32536e9i) q^{20} -3.46029e9i q^{22} +1.25080e10i q^{23} +(-9.77005e9 - 2.89114e10i) q^{25} +4.26411e10 q^{26} +1.40805e10i q^{28} +5.43807e10 q^{29} +1.05351e11 q^{31} -3.43597e10i q^{32} +1.36709e11 q^{34} +(1.21975e11 + 8.75322e10i) q^{35} -1.33702e11i q^{37} +2.94193e11i q^{38} +(-2.97647e11 - 2.13598e11i) q^{40} +1.24268e12 q^{41} +4.58396e11i q^{43} -4.42917e11 q^{44} +1.60102e12 q^{46} -2.31085e12i q^{47} +4.00898e12 q^{49} +(-3.70066e12 + 1.25057e12i) q^{50} -5.45806e12i q^{52} -1.66620e12i q^{53} +(-2.75341e12 + 3.83683e12i) q^{55} +1.80231e12 q^{56} -6.96073e12i q^{58} -2.60140e13 q^{59} -1.95306e13 q^{61} -1.34850e13i q^{62} -4.39805e12 q^{64} +(-4.72813e13 - 3.39302e13i) q^{65} +2.32062e13i q^{67} -1.74987e13i q^{68} +(1.12041e13 - 1.56128e13i) q^{70} +8.64331e13 q^{71} +1.28307e14i q^{73} -1.71139e13 q^{74} +3.76567e13 q^{76} -2.32328e13i q^{77} -1.07394e14 q^{79} +(-2.73406e13 + 3.80988e13i) q^{80} -1.59063e14i q^{82} -2.06951e14i q^{83} +(-1.51585e14 - 1.08781e14i) q^{85} +5.86747e13 q^{86} +5.66933e13i q^{88} -3.44568e14 q^{89} +2.86298e14 q^{91} -2.04931e14i q^{92} -2.95788e14 q^{94} +(2.34094e14 - 3.26207e14i) q^{95} +5.81892e14i q^{97} -5.13149e14i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 262144 q^{4} - 49733632 q^{10} + 4294967296 q^{16} - 9028552704 q^{19} + 42419563632 q^{25} - 40724611904 q^{31} - 885646311424 q^{34} + 814835826688 q^{40} - 654599782400 q^{46} - 17251393932048 q^{49}+ \cdots - 909200639590400 q^{94}+O(q^{100}) $ 16 * q - 262144 * q^4 - 49733632 * q^10 + 4294967296 * q^16 - 9028552704 * q^19 + 42419563632 * q^25 - 40724611904 * q^31 - 885646311424 * q^34 + 814835826688 * q^40 - 654599782400 * q^46 - 17251393932048 * q^49 + 11333866801472 * q^55 + 92663079527072 * q^61 - 70368744177664 * q^64 - 33467474673664 * q^70 + 147923807502336 * q^76 + 543959857901376 * q^79 - 1590761422616992 * q^85 + 2706439057736832 * q^91 - 909200639590400 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	128.000i		−	0.707107i
$2$		−	128.000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−16384.0			−0.500000
$5$	−101852.	+	141929.i	−0.583033	+	0.812449i
$5$	−101852.	+	141929.i	−0.583033	+	0.812449i
$6$		0			0
$7$		−	859408.i		−	0.394425i	−0.980361	−	0.197212i	$-0.936811\pi$
$7$		−	859408.i		−	0.394425i	0.980361	−	0.197212i	$-0.0631889\pi$
$8$			2.09715e6i			0.353553i
$9$		0			0
$10$	1.81669e7	+	1.30370e7i	0.574488	+	0.412267i
$11$	2.70335e7			0.418270			0.209135	−	0.977887i	$-0.432935\pi$
$11$	2.70335e7			0.418270			0.209135	+	0.977887i	$0.432935\pi$
$12$		0			0
$13$			3.33134e8i			1.47246i	0.676732	+	0.736230i	$0.263396\pi$
$13$			3.33134e8i			1.47246i	−0.676732	+	0.736230i	$0.736604\pi$
$14$	−1.10004e8			−0.278900
$15$		0			0
$16$	2.68435e8			0.250000
$17$			1.06804e9i			0.631276i	0.948880	+	0.315638i	$0.102219\pi$
$17$			1.06804e9i			0.631276i	−0.948880	+	0.315638i	$0.897781\pi$
$18$		0			0
$19$	−2.29839e9			−0.589890			−0.294945	−	0.955514i	$-0.595301\pi$
$19$	−2.29839e9			−0.589890			−0.294945	+	0.955514i	$0.595301\pi$
$20$	1.66874e9	−	2.32536e9i	0.291516	−	0.406224i
$21$		0			0
$22$		−	3.46029e9i		−	0.295762i
$23$			1.25080e10i			0.766000i	0.923748	+	0.383000i	$0.125109\pi$
$23$			1.25080e10i			0.766000i	−0.923748	+	0.383000i	$0.874891\pi$
$24$		0			0
$25$	−9.77005e9	−	2.89114e10i	−0.320145	−	0.947369i
$26$	4.26411e10			1.04119
$27$		0			0
$28$			1.40805e10i			0.197212i
$29$	5.43807e10			0.585409			0.292705	−	0.956203i	$-0.405445\pi$
$29$	5.43807e10			0.585409			0.292705	+	0.956203i	$0.405445\pi$
$30$		0			0
$31$	1.05351e11			0.687745			0.343873	−	0.939016i	$-0.388261\pi$
$31$	1.05351e11			0.687745			0.343873	+	0.939016i	$0.388261\pi$
$32$		−	3.43597e10i		−	0.176777i
$33$		0			0
$34$	1.36709e11			0.446380
$35$	1.21975e11	+	8.75322e10i	0.320450	+	0.229963i
$36$		0			0
$37$		−	1.33702e11i		−	0.231540i	−0.993276	−	0.115770i	$-0.963066\pi$
$37$		−	1.33702e11i		−	0.231540i	0.993276	−	0.115770i	$-0.0369336\pi$
$38$			2.94193e11i			0.417115i
$39$		0			0
$40$	−2.97647e11	−	2.13598e11i	−0.287244	−	0.206133i
$41$	1.24268e12			0.996505			0.498253	−	0.867032i	$-0.333975\pi$
$41$	1.24268e12			0.996505			0.498253	+	0.867032i	$0.333975\pi$
$42$		0			0
$43$			4.58396e11i			0.257174i	0.991698	+	0.128587i	$0.0410442\pi$
$43$			4.58396e11i			0.257174i	−0.991698	+	0.128587i	$0.958956\pi$
$44$	−4.42917e11			−0.209135
$45$		0			0
$46$	1.60102e12			0.541643
$47$		−	2.31085e12i		−	0.665330i	−0.943045	−	0.332665i	$-0.892052\pi$
$47$		−	2.31085e12i		−	0.665330i	0.943045	−	0.332665i	$-0.107948\pi$
$48$		0			0
$49$	4.00898e12			0.844429
$50$	−3.70066e12	+	1.25057e12i	−0.669891	+	0.226377i
$51$		0			0
$52$		−	5.45806e12i		−	0.736230i
$53$		−	1.66620e12i		−	0.194832i	−0.995244	−	0.0974158i	$-0.968942\pi$
$53$		−	1.66620e12i		−	0.194832i	0.995244	−	0.0974158i	$-0.0310577\pi$
$54$		0			0
$55$	−2.75341e12	+	3.83683e12i	−0.243865	+	0.339823i
$56$	1.80231e12			0.139450
$57$		0			0
$58$		−	6.96073e12i		−	0.413947i
$59$	−2.60140e13			−1.36087			−0.680436	−	0.732807i	$-0.738210\pi$
$59$	−2.60140e13			−1.36087			−0.680436	+	0.732807i	$0.738210\pi$
$60$		0			0
$61$	−1.95306e13			−0.795688			−0.397844	−	0.917453i	$-0.630241\pi$
$61$	−1.95306e13			−0.795688			−0.397844	+	0.917453i	$0.630241\pi$
$62$		−	1.34850e13i		−	0.486309i
$63$		0			0
$64$	−4.39805e12			−0.125000
$65$	−4.72813e13	−	3.39302e13i	−1.19630	−	0.858492i
$66$		0			0
$67$			2.32062e13i			0.467781i	0.972263	+	0.233891i	$0.0751458\pi$
$67$			2.32062e13i			0.467781i	−0.972263	+	0.233891i	$0.924854\pi$
$68$		−	1.74987e13i		−	0.315638i
$69$		0			0
$70$	1.12041e13	−	1.56128e13i	0.162608	−	0.226592i
$71$	8.64331e13			1.12783			0.563914	−	0.825834i	$-0.309295\pi$
$71$	8.64331e13			1.12783			0.563914	+	0.825834i	$0.309295\pi$
$72$		0			0
$73$			1.28307e14i			1.35934i	0.733517	+	0.679671i	$0.237877\pi$
$73$			1.28307e14i			1.35934i	−0.733517	+	0.679671i	$0.762123\pi$
$74$	−1.71139e13			−0.163724
$75$		0			0
$76$	3.76567e13			0.294945
$77$		−	2.32328e13i		−	0.164976i
$78$		0			0
$79$	−1.07394e14			−0.629182			−0.314591	−	0.949227i	$-0.601867\pi$
$79$	−1.07394e14			−0.629182			−0.314591	+	0.949227i	$0.601867\pi$
$80$	−2.73406e13	+	3.80988e13i	−0.145758	+	0.203112i
$81$		0			0
$82$		−	1.59063e14i		−	0.704636i
$83$		−	2.06951e14i		−	0.837110i	−0.908192	−	0.418555i	$-0.862537\pi$
$83$		−	2.06951e14i		−	0.837110i	0.908192	−	0.418555i	$-0.137463\pi$
$84$		0			0
$85$	−1.51585e14	−	1.08781e14i	−0.512880	−	0.368055i
$86$	5.86747e13			0.181850
$87$		0			0
$88$			5.66933e13i			0.147881i
$89$	−3.44568e14			−0.825753			−0.412876	−	0.910787i	$-0.635476\pi$
$89$	−3.44568e14			−0.825753			−0.412876	+	0.910787i	$0.635476\pi$
$90$		0			0
$91$	2.86298e14			0.580774
$92$		−	2.04931e14i		−	0.383000i
$93$		0			0
$94$	−2.95788e14			−0.470459
$95$	2.34094e14	−	3.26207e14i	0.343925	−	0.479255i
$96$		0			0
$97$			5.81892e14i			0.731230i	0.930766	+	0.365615i	$0.119141\pi$
$97$			5.81892e14i			0.731230i	−0.930766	+	0.365615i	$0.880859\pi$
$98$		−	5.13149e14i		−	0.597101i
$99$		0			0
$100$	1.60073e14	+	4.73684e14i	0.160073	+	0.473684i
$101$	−1.85306e15			−1.71980			−0.859901	−	0.510460i	$-0.829475\pi$
$101$	−1.85306e15			−1.71980			−0.859901	+	0.510460i	$0.829475\pi$
$102$		0			0
$103$		−	8.03061e14i		−	0.643383i	−0.946845	−	0.321691i	$-0.895749\pi$
$103$		−	8.03061e14i		−	0.643383i	0.946845	−	0.321691i	$-0.104251\pi$
$104$	−6.98632e14			−0.520593
$105$		0			0
$106$	−2.13274e14			−0.137767
$107$		−	1.84838e15i		−	1.11279i	−0.830917	−	0.556396i	$-0.812184\pi$
$107$		−	1.84838e15i		−	1.11279i	0.830917	−	0.556396i	$-0.187816\pi$
$108$		0			0
$109$	2.21824e14			0.116228			0.0581139	−	0.998310i	$-0.481491\pi$
$109$	2.21824e14			0.116228			0.0581139	+	0.998310i	$0.481491\pi$
$110$	4.91115e14	+	3.52436e14i	0.240291	+	0.172439i
$111$		0			0
$112$		−	2.30696e14i		−	0.0986062i
$113$			1.20483e15i			0.481767i	0.970554	+	0.240884i	$0.0774372\pi$
$113$			1.20483e15i			0.481767i	−0.970554	+	0.240884i	$0.922563\pi$
$114$		0			0
$115$	−1.77524e15	−	1.27396e15i	−0.622335	−	0.446603i
$116$	−8.90973e14			−0.292705
$117$		0			0
$118$			3.32980e15i			0.962282i
$119$	9.17880e14			0.248991
$120$		0			0
$121$	−3.44644e15			−0.825050
$122$			2.49992e15i			0.562636i
$123$		0			0
$124$	−1.72608e15			−0.343873
$125$	5.09846e15	+	1.55802e15i	0.956343	+	0.292246i
$126$		0			0
$127$			7.86228e15i			1.30924i	0.755956	+	0.654622i	$0.227172\pi$
$127$			7.86228e15i			1.30924i	−0.755956	+	0.654622i	$0.772828\pi$
$128$			5.62950e14i			0.0883883i
$129$		0			0
$130$	−4.34307e15	+	6.05200e15i	−0.607046	+	0.845910i
$131$	6.42621e15			0.848047			0.424024	−	0.905651i	$-0.360617\pi$
$131$	6.42621e15			0.848047			0.424024	+	0.905651i	$0.360617\pi$
$132$		0			0
$133$			1.97525e15i			0.232667i
$134$	2.97039e15			0.330771
$135$		0			0
$136$	−2.23984e15			−0.223190
$137$			6.62688e15i			0.625036i	0.949912	+	0.312518i	$0.101172\pi$
$137$			6.62688e15i			0.625036i	−0.949912	+	0.312518i	$0.898828\pi$
$138$		0			0
$139$	−2.07903e16			−1.75893			−0.879467	−	0.475960i	$-0.842101\pi$
$139$	−2.07903e16			−1.75893			−0.879467	+	0.475960i	$0.842101\pi$
$140$	−1.99844e15	−	1.43413e15i	−0.160225	−	0.114981i
$141$		0			0
$142$		−	1.10634e16i		−	0.797494i
$143$			9.00576e15i			0.615886i
$144$		0			0
$145$	−5.53876e15	+	7.71819e15i	−0.341313	+	0.475615i
$146$	1.64233e16			0.961200
$147$		0			0
$148$			2.19058e15i			0.115770i
$149$	−1.27967e16			−0.642984			−0.321492	−	0.946912i	$-0.604184\pi$
$149$	−1.27967e16			−0.642984			−0.321492	+	0.946912i	$0.604184\pi$
$150$		0			0
$151$	−1.91509e16			−0.870686			−0.435343	−	0.900265i	$-0.643373\pi$
$151$	−1.91509e16			−0.870686			−0.435343	+	0.900265i	$0.643373\pi$
$152$		−	4.82006e15i		−	0.208558i
$153$		0			0
$154$	−2.97380e15			−0.116656
$155$	−1.07302e16	+	1.49524e16i	−0.400978	+	0.558757i
$156$		0			0
$157$			5.45855e16i			1.85281i	0.376534	+	0.926403i	$0.377116\pi$
$157$			5.45855e16i			1.85281i	−0.376534	+	0.926403i	$0.622884\pi$
$158$			1.37464e16i			0.444899i
$159$		0			0
$160$	4.87664e15	+	3.49960e15i	0.143622	+	0.103067i
$161$	1.07495e16			0.302129
$162$		0			0
$163$			3.55499e16i			0.910817i	0.890282	+	0.455409i	$0.150507\pi$
$163$			3.55499e16i			0.910817i	−0.890282	+	0.455409i	$0.849493\pi$
$164$	−2.03600e16			−0.498253
$165$		0			0
$166$	−2.64898e16			−0.591926
$167$		−	2.57661e16i		−	0.550396i	−0.961388	−	0.275198i	$-0.911257\pi$
$167$		−	2.57661e16i		−	0.550396i	0.961388	−	0.275198i	$-0.0887435\pi$
$168$		0			0
$169$	−5.97921e16			−1.16814
$170$	−1.39240e16	+	1.94029e16i	−0.260254	+	0.362661i
$171$		0			0
$172$		−	7.51036e15i		−	0.128587i
$173$		−	3.02340e16i		−	0.495622i	−0.968808	−	0.247811i	$-0.920289\pi$
$173$		−	3.02340e16i		−	0.495622i	0.968808	−	0.247811i	$-0.0797112\pi$
$174$		0			0
$175$	−2.48467e16	+	8.39647e15i	−0.373666	+	0.126273i
$176$	7.25675e15			0.104568
$177$		0			0
$178$			4.41047e16i			0.583895i
$179$	5.56050e16			0.705855			0.352928	−	0.935651i	$-0.385186\pi$
$179$	5.56050e16			0.705855			0.352928	+	0.935651i	$0.385186\pi$
$180$		0			0
$181$	−1.60583e17			−1.87547			−0.937734	−	0.347355i	$-0.887080\pi$
$181$	−1.60583e17			−1.87547			−0.937734	+	0.347355i	$0.887080\pi$
$182$		−	3.66461e16i		−	0.410670i
$183$		0			0
$184$	−2.62311e16			−0.270822
$185$	1.89762e16	+	1.36178e16i	0.188114	+	0.134996i
$186$		0			0
$187$			2.88728e16i			0.264044i
$188$			3.78609e16i			0.332665i
$189$		0			0
$190$	−4.17545e16	−	2.99641e16i	−0.338884	−	0.243192i
$191$	−1.51816e17			−1.18459			−0.592294	−	0.805722i	$-0.701777\pi$
$191$	−1.51816e17			−1.18459			−0.592294	+	0.805722i	$0.701777\pi$
$192$		0			0
$193$			1.44443e17i			1.04236i	0.853448	+	0.521179i	$0.174507\pi$
$193$			1.44443e17i			1.04236i	−0.853448	+	0.521179i	$0.825493\pi$
$194$	7.44822e16			0.517058
$195$		0			0
$196$	−6.56831e16			−0.422215
$197$		−	1.69239e17i		−	1.04714i	−0.851984	−	0.523568i	$-0.824601\pi$
$197$		−	1.69239e17i		−	1.04714i	0.851984	−	0.523568i	$-0.175399\pi$
$198$		0			0
$199$	−1.12029e17			−0.642587			−0.321294	−	0.946980i	$-0.604118\pi$
$199$	−1.12029e17			−0.642587			−0.321294	+	0.946980i	$0.604118\pi$
$200$	6.06316e16	−	2.04893e16i	0.334945	−	0.113188i
$201$		0			0
$202$			2.37191e17i			1.21608i
$203$		−	4.67352e16i		−	0.230900i
$204$		0			0
$205$	−1.26569e17	+	1.76372e17i	−0.580995	+	0.809609i
$206$	−1.02792e17			−0.454940
$207$		0			0
$208$			8.94249e16i			0.368115i
$209$	−6.21334e16			−0.246733
$210$		0			0
$211$	−6.14009e16			−0.227016			−0.113508	−	0.993537i	$-0.536209\pi$
$211$	−6.14009e16			−0.227016			−0.113508	+	0.993537i	$0.536209\pi$
$212$			2.72991e16i			0.0974158i
$213$		0			0
$214$	−2.36593e17			−0.786862
$215$	−6.50597e16	−	4.66884e16i	−0.208941	−	0.149941i
$216$		0			0
$217$		−	9.05399e16i		−	0.271264i
$218$		−	2.83935e16i		−	0.0821854i
$219$		0			0
$220$	4.51118e16	−	6.28627e16i	0.121933	−	0.169911i
$221$	−3.55799e17			−0.929529
$222$		0			0
$223$		−	3.63890e17i		−	0.888553i	−0.895890	−	0.444277i	$-0.853461\pi$
$223$		−	3.63890e17i		−	0.888553i	0.895890	−	0.444277i	$-0.146539\pi$
$224$	−2.95290e16			−0.0697251
$225$		0			0
$226$	1.54218e17			0.340661
$227$		−	6.60092e17i		−	1.41062i	−0.708899	−	0.705310i	$-0.750808\pi$
$227$		−	6.60092e17i		−	1.41062i	0.708899	−	0.705310i	$-0.249192\pi$
$228$		0			0
$229$	−2.90949e16			−0.0582171			−0.0291086	−	0.999576i	$-0.509267\pi$
$229$	−2.90949e16			−0.0582171			−0.0291086	+	0.999576i	$0.509267\pi$
$230$	−1.63067e17	+	2.27231e17i	−0.315796	+	0.440057i
$231$		0			0
$232$			1.14045e17i			0.206973i
$233$			1.46706e17i			0.257798i	0.991658	+	0.128899i	$0.0411443\pi$
$233$			1.46706e17i			0.257798i	−0.991658	+	0.128899i	$0.958856\pi$
$234$		0			0
$235$	3.27976e17	+	2.35363e17i	0.540546	+	0.387909i
$236$	4.26214e17			0.680436
$237$		0			0
$238$		−	1.17489e17i		−	0.176063i
$239$	−2.90604e17			−0.422005			−0.211002	−	0.977486i	$-0.567673\pi$
$239$	−2.90604e17			−0.422005			−0.211002	+	0.977486i	$0.567673\pi$
$240$		0			0
$241$	3.82729e17			0.522112			0.261056	−	0.965324i	$-0.415929\pi$
$241$	3.82729e17			0.522112			0.261056	+	0.965324i	$0.415929\pi$
$242$			4.41144e17i			0.583399i
$243$		0			0
$244$	3.19990e17			0.397844
$245$	−4.08321e17	+	5.68990e17i	−0.492330	+	0.686055i
$246$		0			0
$247$		−	7.65669e17i		−	0.868588i
$248$			2.20938e17i			0.243155i
$249$		0			0
$250$	1.99427e17	−	6.52603e17i	0.206649	−	0.676237i
$251$	1.84707e18			1.85751			0.928753	−	0.370700i	$-0.120882\pi$
$251$	1.84707e18			1.85751			0.928753	+	0.370700i	$0.120882\pi$
$252$		0			0
$253$			3.38134e17i			0.320395i
$254$	1.00637e18			0.925775
$255$		0			0
$256$	7.20576e16			0.0625000
$257$		−	1.17826e16i		−	0.00992529i	−0.999988	−	0.00496264i	$-0.998420\pi$
$257$		−	1.17826e16i		−	0.00992529i	0.999988	−	0.00496264i	$-0.00157967\pi$
$258$		0			0
$259$	−1.14905e17			−0.0913252
$260$	7.74657e17	+	5.55913e17i	0.598149	+	0.429246i
$261$		0			0
$262$		−	8.22555e17i		−	0.599660i
$263$			6.41407e17i			0.454428i	0.973845	+	0.227214i	$0.0729617\pi$
$263$			6.41407e17i			0.454428i	−0.973845	+	0.227214i	$0.927038\pi$
$264$		0			0
$265$	2.36483e17	+	1.69706e17i	0.158291	+	0.113593i
$266$	2.52832e17			0.164521
$267$		0			0
$268$		−	3.80210e17i		−	0.233891i
$269$	2.41211e16			0.0144296			0.00721482	−	0.999974i	$-0.497703\pi$
$269$	2.41211e16			0.0144296			0.00721482	+	0.999974i	$0.497703\pi$
$270$		0			0
$271$	2.86280e18			1.62002			0.810011	−	0.586415i	$-0.199461\pi$
$271$	2.86280e18			1.62002			0.810011	+	0.586415i	$0.199461\pi$
$272$			2.86699e17i			0.157819i
$273$		0			0
$274$	8.48241e17			0.441967
$275$	−2.64119e17	−	7.81576e17i	−0.133907	−	0.396256i
$276$		0			0
$277$			1.70365e18i			0.818053i	0.912523	+	0.409026i	$0.134132\pi$
$277$			1.70365e18i			0.818053i	−0.912523	+	0.409026i	$0.865868\pi$
$278$			2.66116e18i			1.24375i
$279$		0			0
$280$	−1.83568e17	+	2.55800e17i	−0.0813041	+	0.113296i
$281$	−1.55561e18			−0.670815			−0.335408	−	0.942073i	$-0.608874\pi$
$281$	−1.55561e18			−0.670815			−0.335408	+	0.942073i	$0.608874\pi$
$282$		0			0
$283$		−	3.94412e18i		−	1.61270i	−0.591442	−	0.806348i	$-0.701441\pi$
$283$		−	3.94412e18i		−	1.61270i	0.591442	−	0.806348i	$-0.298559\pi$
$284$	−1.41612e18			−0.563914
$285$		0			0
$286$	1.15274e18			0.435497
$287$		−	1.06797e18i		−	0.393047i
$288$		0			0
$289$	1.72172e18			0.601490
$290$	9.87928e17	+	7.08961e17i	0.336310	+	0.241345i
$291$		0			0
$292$		−	2.10218e18i		−	0.679671i
$293$		−	5.07795e18i		−	1.60022i	−0.599850	−	0.800112i	$-0.704773\pi$
$293$		−	5.07795e18i		−	1.60022i	0.599850	−	0.800112i	$-0.295227\pi$
$294$		0			0
$295$	2.64957e18	−	3.69214e18i	0.793434	−	1.10564i
$296$	2.80394e17			0.0818618
$297$		0			0
$298$			1.63797e18i			0.454658i
$299$	−4.16683e18			−1.12790
$300$		0			0
$301$	3.93950e17			0.101436
$302$			2.45131e18i			0.615668i
$303$		0			0
$304$	−6.16968e17			−0.147472
$305$	1.98923e18	−	2.77196e18i	0.463912	−	0.646455i
$306$		0			0
$307$		−	4.64657e18i		−	1.03180i	−0.856649	−	0.515899i	$-0.827458\pi$
$307$		−	4.64657e18i		−	1.03180i	0.856649	−	0.515899i	$-0.172542\pi$
$308$			3.80646e17i			0.0824881i
$309$		0			0
$310$	1.91391e18	+	1.37347e18i	0.395101	+	0.283534i
$311$	−8.91857e18			−1.79718			−0.898591	−	0.438787i	$-0.855408\pi$
$311$	−8.91857e18			−1.79718			−0.898591	+	0.438787i	$0.855408\pi$
$312$		0			0
$313$		−	8.86194e16i		−	0.0170195i	−0.999964	−	0.00850974i	$-0.997291\pi$
$313$		−	8.86194e16i		−	0.0170195i	0.999964	−	0.00850974i	$-0.00270877\pi$
$314$	6.98694e18			1.31013
$315$		0			0
$316$	1.75954e18			0.314591
$317$		−	2.49965e18i		−	0.436450i	−0.975898	−	0.218225i	$-0.929973\pi$
$317$		−	2.49965e18i		−	0.436450i	0.975898	−	0.218225i	$-0.0700266\pi$
$318$		0			0
$319$	1.47010e18			0.244859
$320$	4.47948e17	−	6.24210e17i	0.0728791	−	0.101556i
$321$		0			0
$322$		−	1.37593e18i		−	0.213638i
$323$		−	2.45476e18i		−	0.372383i
$324$		0			0
$325$	9.63135e18	−	3.25473e18i	1.39496	−	0.471401i
$326$	4.55039e18			0.644045
$327$		0			0
$328$			2.60608e18i			0.352318i
$329$	−1.98596e18			−0.262423
$330$		0			0
$331$	7.07818e18			0.893740			0.446870	−	0.894599i	$-0.352539\pi$
$331$	7.07818e18			0.893740			0.446870	+	0.894599i	$0.352539\pi$
$332$			3.39069e18i			0.418555i
$333$		0			0
$334$	−3.29806e18			−0.389189
$335$	−3.29363e18	−	2.36359e18i	−0.380048	−	0.272732i
$336$		0			0
$337$			1.78640e18i			0.197131i	0.995131	+	0.0985655i	$0.0314254\pi$
$337$			1.78640e18i			0.197131i	−0.995131	+	0.0985655i	$0.968575\pi$
$338$			7.65339e18i			0.825997i
$339$		0			0
$340$	2.48357e18	+	1.78227e18i	0.256440	+	0.184027i
$341$	2.84801e18			0.287663
$342$		0			0
$343$		−	7.52544e18i		−	0.727489i
$344$	−9.61327e17			−0.0909249
$345$		0			0
$346$	−3.86996e18			−0.350457
$347$		−	1.31311e19i		−	1.16367i	−0.813306	−	0.581837i	$-0.802334\pi$
$347$		−	1.31311e19i		−	1.16367i	0.813306	−	0.581837i	$-0.197666\pi$
$348$		0			0
$349$	−1.61974e19			−1.37485			−0.687423	−	0.726258i	$-0.741258\pi$
$349$	−1.61974e19			−1.37485			−0.687423	+	0.726258i	$0.741258\pi$
$350$	1.07475e18	+	3.18038e18i	0.0892886	+	0.264222i
$351$		0			0
$352$		−	9.28863e17i		−	0.0739404i
$353$		−	1.71943e19i		−	1.33990i	−0.742404	−	0.669952i	$-0.766315\pi$
$353$		−	1.71943e19i		−	1.33990i	0.742404	−	0.669952i	$-0.233685\pi$
$354$		0			0
$355$	−8.80336e18	+	1.22674e19i	−0.657560	+	0.916301i
$356$	5.64540e18			0.412876
$357$		0			0
$358$		−	7.11743e18i		−	0.499115i
$359$	−4.25951e18			−0.292517			−0.146259	−	0.989246i	$-0.546723\pi$
$359$	−4.25951e18			−0.292517			−0.146259	+	0.989246i	$0.546723\pi$
$360$		0			0
$361$	−9.89855e18			−0.652030
$362$			2.05546e19i			1.32616i
$363$		0			0
$364$	−4.69070e18			−0.290387
$365$	−1.82105e19	−	1.30683e19i	−1.10440	−	0.792541i
$366$		0			0
$367$			1.68237e19i			0.979326i	0.871912	+	0.489663i	$0.162880\pi$
$367$			1.68237e19i			0.979326i	−0.871912	+	0.489663i	$0.837120\pi$
$368$			3.35759e18i			0.191500i
$369$		0			0
$370$	1.74308e18	−	2.42896e18i	0.0954563	−	0.133017i
$371$	−1.43195e18			−0.0768464
$372$		0			0
$373$			2.75947e19i			1.42236i	0.703011	+	0.711179i	$0.251838\pi$
$373$			2.75947e19i			1.42236i	−0.703011	+	0.711179i	$0.748162\pi$
$374$	3.69571e18			0.186707
$375$		0			0
$376$	4.84619e18			0.235230
$377$			1.81160e19i			0.861991i
$378$		0			0
$379$	−3.23762e19			−1.48058			−0.740290	−	0.672287i	$-0.765312\pi$
$379$	−3.23762e19			−1.48058			−0.740290	+	0.672287i	$0.765312\pi$
$380$	−3.83540e18	+	5.34458e18i	−0.171963	+	0.239628i
$381$		0			0
$382$			1.94324e19i			0.837630i
$383$			7.04626e18i			0.297830i	0.988850	+	0.148915i	$0.0475780\pi$
$383$			7.04626e18i			0.297830i	−0.988850	+	0.148915i	$0.952422\pi$
$384$		0			0
$385$	3.29741e18	+	2.36630e18i	0.134035	+	0.0961865i
$386$	1.84887e19			0.737058
$387$		0			0
$388$		−	9.53372e18i		−	0.365615i
$389$	−5.85397e18			−0.220206			−0.110103	−	0.993920i	$-0.535118\pi$
$389$	−5.85397e18			−0.220206			−0.110103	+	0.993920i	$0.535118\pi$
$390$		0			0
$391$	−1.33590e19			−0.483557
$392$			8.40744e18i			0.298551i
$393$		0			0
$394$	−2.16625e19			−0.740437
$395$	1.09382e19	−	1.52423e19i	0.366834	−	0.511178i
$396$		0			0
$397$		−	1.70576e19i		−	0.550795i	−0.961330	−	0.275398i	$-0.911191\pi$
$397$		−	1.70576e19i		−	0.550795i	0.961330	−	0.275398i	$-0.0888095\pi$
$398$			1.43397e19i			0.454378i
$399$		0			0
$400$	−2.62263e18	−	7.76084e18i	−0.0800363	−	0.236842i
$401$	−2.11603e19			−0.633780			−0.316890	−	0.948462i	$-0.602639\pi$
$401$	−2.11603e19			−0.633780			−0.316890	+	0.948462i	$0.602639\pi$
$402$		0			0
$403$			3.50961e19i			1.01268i
$404$	3.03605e19			0.859901
$405$		0			0
$406$	−5.98211e18			−0.163271
$407$		−	3.61444e18i		−	0.0968463i
$408$		0			0
$409$	−6.47265e19			−1.67170			−0.835849	−	0.548960i	$-0.815024\pi$
$409$	−6.47265e19			−1.67170			−0.835849	+	0.548960i	$0.815024\pi$
$410$	2.25756e19	+	1.62008e19i	0.572480	+	0.410826i
$411$		0			0
$412$			1.31574e19i			0.321691i
$413$			2.23567e19i			0.536762i
$414$		0			0
$415$	2.93724e19	+	2.10783e19i	0.680108	+	0.488062i
$416$	1.14464e19			0.260296
$417$		0			0
$418$			7.95307e18i			0.174467i
$419$	4.27154e19			0.920407			0.460203	−	0.887814i	$-0.347777\pi$
$419$	4.27154e19			0.920407			0.460203	+	0.887814i	$0.347777\pi$
$420$		0			0
$421$	1.54679e19			0.321601			0.160800	−	0.986987i	$-0.448592\pi$
$421$	1.54679e19			0.321601			0.160800	+	0.986987i	$0.448592\pi$
$422$			7.85931e18i			0.160524i
$423$		0			0
$424$	3.49428e18			0.0688833
$425$	3.08784e19	−	1.04348e19i	0.598051	−	0.202100i
$426$		0			0
$427$			1.67848e19i			0.313839i
$428$			3.02839e19i			0.556396i
$429$		0			0
$430$	−5.97612e18	+	8.32764e18i	−0.106024	+	0.147744i
$431$	−2.89773e19			−0.505217			−0.252609	−	0.967569i	$-0.581289\pi$
$431$	−2.89773e19			−0.505217			−0.252609	+	0.967569i	$0.581289\pi$
$432$		0			0
$433$			1.87806e19i			0.316264i	0.987418	+	0.158132i	$0.0505472\pi$
$433$			1.87806e19i			0.316264i	−0.987418	+	0.158132i	$0.949453\pi$
$434$	−1.15891e19			−0.191812
$435$		0			0
$436$	−3.63436e18			−0.0581139
$437$		−	2.87482e19i		−	0.451855i
$438$		0			0
$439$	−1.15218e20			−1.74999			−0.874994	−	0.484135i	$-0.839135\pi$
$439$	−1.15218e20			−1.74999			−0.874994	+	0.484135i	$0.839135\pi$
$440$	−8.04642e18	−	5.77431e18i	−0.120146	−	0.0862194i
$441$		0			0
$442$			4.55423e19i			0.657276i
$443$		−	5.72248e19i		−	0.812000i	−0.913873	−	0.406000i	$-0.866923\pi$
$443$		−	5.72248e19i		−	0.812000i	0.913873	−	0.406000i	$-0.133077\pi$
$444$		0			0
$445$	3.50948e19	−	4.89042e19i	0.481441	−	0.670882i
$446$	−4.65779e19			−0.628302
$447$		0			0
$448$			3.77972e18i			0.0493031i
$449$	−7.48033e19			−0.959562			−0.479781	−	0.877388i	$-0.659284\pi$
$449$	−7.48033e19			−0.959562			−0.479781	+	0.877388i	$0.659284\pi$
$450$		0			0
$451$	3.35939e19			0.416808
$452$		−	1.97399e19i		−	0.240884i
$453$		0			0
$454$	−8.44917e19			−0.997460
$455$	−2.91599e19	+	4.06339e19i	−0.338611	+	0.471849i
$456$		0			0
$457$		−	7.11712e19i		−	0.799711i	−0.916578	−	0.399855i	$-0.869060\pi$
$457$		−	7.11712e19i		−	0.799711i	0.916578	−	0.399855i	$-0.130940\pi$
$458$			3.72415e18i			0.0411657i
$459$		0			0
$460$	2.90856e19	+	2.08725e19i	0.311168	+	0.223301i
$461$	7.11766e18			0.0749170			0.0374585	−	0.999298i	$-0.488074\pi$
$461$	7.11766e18			0.0749170			0.0374585	+	0.999298i	$0.488074\pi$
$462$		0			0
$463$		−	7.40604e19i		−	0.754621i	−0.926087	−	0.377310i	$-0.876849\pi$
$463$		−	7.40604e19i		−	0.754621i	0.926087	−	0.377310i	$-0.123151\pi$
$464$	1.45977e19			0.146352
$465$		0			0
$466$	1.87784e19			0.182291
$467$		−	1.02562e20i		−	0.979740i	−0.871795	−	0.489870i	$-0.837044\pi$
$467$		−	1.02562e20i		−	0.979740i	0.871795	−	0.489870i	$-0.162956\pi$
$468$		0			0
$469$	1.99436e19			0.184505
$470$	3.01265e19	−	4.19809e19i	0.274293	−	0.382224i
$471$		0			0
$472$		−	5.45554e19i		−	0.481141i
$473$			1.23920e19i			0.107568i
$474$		0			0
$475$	2.24554e19	+	6.64495e19i	0.188850	+	0.558843i
$476$	−1.50386e19			−0.124496
$477$		0			0
$478$			3.71973e19i			0.298402i
$479$	−2.01268e20			−1.58949			−0.794745	−	0.606944i	$-0.792395\pi$
$479$	−2.01268e20			−1.58949			−0.794745	+	0.606944i	$0.792395\pi$
$480$		0			0
$481$	4.45408e19			0.340933
$482$		−	4.89893e19i		−	0.369189i
$483$		0			0
$484$	5.64665e19			0.412525
$485$	−8.25873e19	−	5.92667e19i	−0.594087	−	0.426331i
$486$		0			0
$487$			1.36673e20i			0.953272i	0.879101	+	0.476636i	$0.158144\pi$
$487$			1.36673e20i			0.953272i	−0.879101	+	0.476636i	$0.841856\pi$
$488$		−	4.09587e19i		−	0.281318i
$489$		0			0
$490$	7.28307e19	+	5.22651e19i	0.485114	+	0.348130i
$491$	1.82306e20			1.19588			0.597941	−	0.801540i	$-0.295986\pi$
$491$	1.82306e20			1.19588			0.597941	+	0.801540i	$0.295986\pi$
$492$		0			0
$493$			5.80806e19i			0.369555i
$494$	−9.80057e19			−0.614185
$495$		0			0
$496$	2.82800e19			0.171936
$497$		−	7.42813e19i		−	0.444843i
$498$		0			0
$499$	6.31125e19			0.366742			0.183371	−	0.983044i	$-0.441299\pi$
$499$	6.31125e19			0.366742			0.183371	+	0.983044i	$0.441299\pi$
$500$	−8.35331e19	−	2.55266e19i	−0.478172	−	0.146123i
$501$		0			0
$502$		−	2.36425e20i		−	1.31345i
$503$			2.02483e20i			1.10823i	0.832441	+	0.554114i	$0.186943\pi$
$503$			2.02483e20i			1.10823i	−0.832441	+	0.554114i	$0.813057\pi$
$504$		0			0
$505$	1.88737e20	−	2.63002e20i	1.00270	−	1.39725i
$506$	4.32812e19			0.226553
$507$		0			0
$508$		−	1.28816e20i		−	0.654622i
$509$	3.75426e20			1.87993			0.939963	−	0.341278i	$-0.110860\pi$
$509$	3.75426e20			1.87993			0.939963	+	0.341278i	$0.110860\pi$
$510$		0			0
$511$	1.10268e20			0.536158
$512$		−	9.22337e18i		−	0.0441942i
$513$		0			0
$514$	−1.50817e18			−0.00701824
$515$	1.13978e20	+	8.17931e19i	0.522715	+	0.375113i
$516$		0			0
$517$		−	6.24702e19i		−	0.278288i
$518$			1.47078e19i			0.0645767i
$519$		0			0
$520$	7.11568e19	−	9.91560e19i	0.303523	−	0.422955i
$521$	5.21506e19			0.219268			0.109634	−	0.993972i	$-0.465032\pi$
$521$	5.21506e19			0.219268			0.109634	+	0.993972i	$0.465032\pi$
$522$		0			0
$523$		−	4.64603e20i		−	1.89810i	−0.315122	−	0.949051i	$-0.602045\pi$
$523$		−	4.64603e20i		−	1.89810i	0.315122	−	0.949051i	$-0.397955\pi$
$524$	−1.05287e20			−0.424024
$525$		0			0
$526$	8.21000e19			0.321329
$527$			1.12519e20i			0.434157i
$528$		0			0
$529$	1.10186e20			0.413245
$530$	2.17223e19	−	3.02698e19i	0.0803225	−	0.111928i
$531$		0			0
$532$		−	3.23625e19i		−	0.116334i
$533$			4.13978e20i			1.46731i
$534$		0			0
$535$	2.62339e20	+	1.88261e20i	0.904086	+	0.648794i
$536$	−4.86669e19			−0.165386
$537$		0			0
$538$		−	3.08750e18i		−	0.0102033i
$539$	1.08377e20			0.353199
$540$		0			0
$541$	2.98521e20			0.946227			0.473113	−	0.881002i	$-0.343130\pi$
$541$	2.98521e20			0.946227			0.473113	+	0.881002i	$0.343130\pi$
$542$		−	3.66438e20i		−	1.14553i
$543$		0			0
$544$	3.66975e19			0.111595
$545$	−2.25931e19	+	3.14832e19i	−0.0677646	+	0.0944291i
$546$		0			0
$547$		−	5.47189e18i		−	0.0159673i	−0.999968	−	0.00798367i	$-0.997459\pi$
$547$		−	5.47189e18i		−	0.0159673i	0.999968	−	0.00798367i	$-0.00254131\pi$
$548$		−	1.08575e20i		−	0.312518i
$549$		0			0
$550$	−1.00042e20	+	3.38072e19i	−0.280195	+	0.0946867i
$551$	−1.24988e20			−0.345327
$552$		0			0
$553$			9.22951e19i			0.248165i
$554$	2.18067e20			0.578451
$555$		0			0
$556$	3.40628e20			0.879467
$557$			2.03377e20i			0.518068i	0.965868	+	0.259034i	$0.0834042\pi$
$557$			2.03377e20i			0.518068i	−0.965868	+	0.259034i	$0.916596\pi$
$558$		0			0
$559$	−1.52707e20			−0.378679
$560$	3.27424e19	+	2.34967e19i	0.0801125	+	0.0574907i
$561$		0			0
$562$			1.99118e20i			0.474338i
$563$			5.03111e20i			1.18264i	0.806438	+	0.591318i	$0.201392\pi$
$563$			5.03111e20i			1.18264i	−0.806438	+	0.591318i	$0.798608\pi$
$564$		0			0
$565$	−1.71000e20	−	1.22714e20i	−0.391411	−	0.280886i
$566$	−5.04848e20			−1.14035
$567$		0			0
$568$			1.81263e20i			0.398747i
$569$	1.59793e19			0.0346909			0.0173455	−	0.999850i	$-0.494478\pi$
$569$	1.59793e19			0.0346909			0.0173455	+	0.999850i	$0.494478\pi$
$570$		0			0
$571$	1.81893e20			0.384633			0.192316	−	0.981333i	$-0.438400\pi$
$571$	1.81893e20			0.384633			0.192316	+	0.981333i	$0.438400\pi$
$572$		−	1.47550e20i		−	0.307943i
$573$		0			0
$574$	−1.36700e20			−0.277926
$575$	3.61623e20	−	1.22204e20i	0.725684	−	0.245231i
$576$		0			0
$577$		−	3.75638e20i		−	0.734431i	−0.930136	−	0.367215i	$-0.880311\pi$
$577$		−	3.75638e20i		−	0.734431i	0.930136	−	0.367215i	$-0.119689\pi$
$578$		−	2.20380e20i		−	0.425318i
$579$		0			0
$580$	9.07471e19	−	1.26455e20i	0.170656	−	0.237807i
$581$	−1.77856e20			−0.330177
$582$		0			0
$583$		−	4.50433e19i		−	0.0814922i
$584$	−2.69079e20			−0.480600
$585$		0			0
$586$	−6.49977e20			−1.13153
$587$			1.37943e20i			0.237090i	0.992949	+	0.118545i	$0.0378231\pi$
$587$			1.37943e20i			0.237090i	−0.992949	+	0.118545i	$0.962177\pi$
$588$		0			0
$589$	−2.42138e20			−0.405694
$590$	−4.72594e20	−	3.39145e20i	−0.781805	−	0.561042i
$591$		0			0
$592$		−	3.58905e19i		−	0.0578850i
$593$			7.57480e20i			1.20632i	0.797622	+	0.603158i	$0.206091\pi$
$593$			7.57480e20i			1.20632i	−0.797622	+	0.603158i	$0.793909\pi$
$594$		0			0
$595$	−9.34876e19	+	1.30274e20i	−0.145170	+	0.202292i
$596$	2.09661e20			0.321492
$597$		0			0
$598$			5.33354e20i			0.797548i
$599$	8.21801e20			1.21357			0.606786	−	0.794865i	$-0.292458\pi$
$599$	8.21801e20			1.21357			0.606786	+	0.794865i	$0.292458\pi$
$600$		0			0
$601$	−3.23051e20			−0.465279			−0.232639	−	0.972563i	$-0.574736\pi$
$601$	−3.23051e20			−0.465279			−0.232639	+	0.972563i	$0.574736\pi$
$602$		−	5.04255e19i		−	0.0717261i
$603$		0			0
$604$	3.13768e20			0.435343
$605$	3.51026e20	−	4.89149e20i	0.481031	−	0.670311i
$606$		0			0
$607$		−	5.29352e20i		−	0.707667i	−0.935308	−	0.353834i	$-0.884878\pi$
$607$		−	5.29352e20i		−	0.707667i	0.935308	−	0.353834i	$-0.115122\pi$
$608$			7.89719e19i			0.104279i
$609$		0			0
$610$	−3.54811e20	−	2.54621e20i	−0.457113	−	0.328035i
$611$	7.69820e20			0.979671
$612$		0			0
$613$			9.88168e20i			1.22709i	0.789659	+	0.613546i	$0.210257\pi$
$613$			9.88168e20i			1.22709i	−0.789659	+	0.613546i	$0.789743\pi$
$614$	−5.94761e20			−0.729591
$615$		0			0
$616$	4.87227e19			0.0583279
$617$			8.93886e19i			0.105717i	0.998602	+	0.0528583i	$0.0168332\pi$
$617$			8.93886e19i			0.105717i	−0.998602	+	0.0528583i	$0.983167\pi$
$618$		0			0
$619$	5.54375e20			0.639917			0.319958	−	0.947432i	$-0.396331\pi$
$619$	5.54375e20			0.639917			0.319958	+	0.947432i	$0.396331\pi$
$620$	1.75804e20	−	2.44980e20i	0.200489	−	0.279379i
$621$		0			0
$622$			1.14158e21i			1.27080i
$623$			2.96125e20i			0.325697i
$624$		0			0
$625$	−7.40415e20	+	5.64932e20i	−0.795014	+	0.606591i
$626$	−1.13433e19			−0.0120346
$627$		0			0
$628$		−	8.94329e20i		−	0.926403i
$629$	1.42799e20			0.146166
$630$		0			0
$631$	−1.05355e21			−1.05302			−0.526508	−	0.850170i	$-0.676499\pi$
$631$	−1.05355e21			−1.05302			−0.526508	+	0.850170i	$0.676499\pi$
$632$		−	2.25221e20i		−	0.222449i
$633$		0			0
$634$	−3.19955e20			−0.308617
$635$	−1.11588e21	−	8.00786e20i	−1.06369	−	0.763332i
$636$		0			0
$637$			1.33553e21i			1.24339i
$638$		−	1.88173e20i		−	0.173142i
$639$		0			0
$640$	−7.98989e19	−	5.73374e19i	−0.0718110	−	0.0515333i
$641$	2.33787e20			0.207675			0.103838	−	0.994594i	$-0.466888\pi$
$641$	2.33787e20			0.207675			0.103838	+	0.994594i	$0.466888\pi$
$642$		0			0
$643$		−	9.14471e20i		−	0.793575i	−0.917911	−	0.396787i	$-0.870125\pi$
$643$		−	9.14471e20i		−	0.793575i	0.917911	−	0.396787i	$-0.129875\pi$
$644$	−1.76119e20			−0.151065
$645$		0			0
$646$	−3.14209e20			−0.263315
$647$			3.67188e20i			0.304163i	0.988368	+	0.152082i	$0.0485976\pi$
$647$			3.67188e20i			0.304163i	−0.988368	+	0.152082i	$0.951402\pi$
$648$		0			0
$649$	−7.03250e20			−0.569212
$650$	−4.16606e20	−	1.23281e21i	−0.333331	−	0.986387i
$651$		0			0
$652$		−	5.82450e20i		−	0.455409i
$653$			2.70806e20i			0.209319i	0.994508	+	0.104660i	$0.0333753\pi$
$653$			2.70806e20i			0.209319i	−0.994508	+	0.104660i	$0.966625\pi$
$654$		0			0
$655$	−6.54520e20	+	9.12065e20i	−0.494440	+	0.688995i
$656$	3.33579e20			0.249126
$657$		0			0
$658$			2.54203e20i			0.185561i
$659$	−2.63065e21			−1.89855			−0.949276	−	0.314444i	$-0.898182\pi$
$659$	−2.63065e21			−1.89855			−0.949276	+	0.314444i	$0.898182\pi$
$660$		0			0
$661$	−8.05298e20			−0.568128			−0.284064	−	0.958805i	$-0.591683\pi$
$661$	−8.05298e20			−0.568128			−0.284064	+	0.958805i	$0.591683\pi$
$662$		−	9.06006e20i		−	0.631970i
$663$		0			0
$664$	4.34008e20			0.295963
$665$	−2.80345e20	−	2.01183e20i	−0.189030	−	0.135653i
$666$		0			0
$667$			6.80192e20i			0.448423i
$668$			4.22152e20i			0.275198i
$669$		0			0
$670$	−3.02539e20	+	4.21585e20i	−0.192851	+	0.268735i
$671$	−5.27981e20			−0.332812
$672$		0			0
$673$			2.04040e21i			1.25778i	0.777496	+	0.628888i	$0.216490\pi$
$673$			2.04040e21i			1.25778i	−0.777496	+	0.628888i	$0.783510\pi$
$674$	2.28660e20			0.139393
$675$		0			0
$676$	9.79633e20			0.584068
$677$		−	2.49652e21i		−	1.47204i	−0.676960	−	0.736019i	$-0.736703\pi$
$677$		−	2.49652e21i		−	1.47204i	0.676960	−	0.736019i	$-0.263297\pi$
$678$		0			0
$679$	5.00083e20			0.288415
$680$	2.28131e20	−	3.17898e20i	0.130127	−	0.181330i
$681$		0			0
$682$		−	3.64546e20i		−	0.203409i
$683$			3.19332e21i			1.76233i	0.472810	+	0.881164i	$0.343240\pi$
$683$			3.19332e21i			1.76233i	−0.472810	+	0.881164i	$0.656760\pi$
$684$		0			0
$685$	−9.40547e20	−	6.74959e20i	−0.507810	−	0.364417i
$686$	−9.63257e20			−0.514412
$687$		0			0
$688$			1.23050e20i			0.0642936i
$689$	5.55069e20			0.286881
$690$		0			0
$691$	−2.76401e21			−1.39783			−0.698915	−	0.715205i	$-0.746333\pi$
$691$	−2.76401e21			−1.39783			−0.698915	+	0.715205i	$0.746333\pi$
$692$			4.95354e20i			0.247811i
$693$		0			0
$694$	−1.68078e21			−0.822841
$695$	2.11753e21	−	2.95074e21i	1.02552	−	1.42904i
$696$		0			0
$697$			1.32723e21i			0.629070i
$698$			2.07326e21i			0.972162i
$699$		0			0
$700$	4.07088e20	−	1.37568e20i	0.186833	−	0.0631366i
$701$	4.85335e20			0.220372			0.110186	−	0.993911i	$-0.464855\pi$
$701$	4.85335e20			0.220372			0.110186	+	0.993911i	$0.464855\pi$
$702$		0			0
$703$			3.07300e20i			0.136583i
$704$	−1.18895e20			−0.0522838
$705$		0			0
$706$	−2.20087e21			−0.947455
$707$			1.59253e21i			0.678333i
$708$		0			0
$709$	1.76272e21			0.735085			0.367542	−	0.930007i	$-0.380199\pi$
$709$	1.76272e21			0.735085			0.367542	+	0.930007i	$0.380199\pi$
$710$	1.57022e21	+	1.12683e21i	0.647923	+	0.464965i
$711$		0			0
$712$		−	7.22612e20i		−	0.291948i
$713$			1.31773e21i			0.526812i
$714$		0			0
$715$	−1.27818e21	−	9.17252e20i	−0.500375	−	0.359082i
$716$	−9.11032e20			−0.352928
$717$		0			0
$718$			5.45218e20i			0.206841i
$719$	2.94680e21			1.10633			0.553163	−	0.833073i	$-0.313421\pi$
$719$	2.94680e21			1.10633			0.553163	+	0.833073i	$0.313421\pi$
$720$		0			0
$721$	−6.90157e20			−0.253766
$722$			1.26701e21i			0.461055i
$723$		0			0
$724$	2.63099e21			0.937734
$725$	−5.31302e20	−	1.57222e21i	−0.187416	−	0.554598i
$726$		0			0
$727$		−	3.91178e19i		−	0.0135166i	−0.999977	−	0.00675829i	$-0.997849\pi$
$727$		−	3.91178e19i		−	0.0135166i	0.999977	−	0.00675829i	$-0.00215125\pi$
$728$			6.00410e20i			0.205335i
$729$		0			0
$730$	−1.67274e21	+	2.33094e21i	−0.560411	+	0.780925i
$731$	−4.89584e20			−0.162348
$732$		0			0
$733$		−	2.31162e21i		−	0.750994i	−0.926824	−	0.375497i	$-0.877472\pi$
$733$		−	2.31162e21i		−	0.750994i	0.926824	−	0.375497i	$-0.122528\pi$
$734$	2.15344e21			0.692488
$735$		0			0
$736$	4.29771e20			0.135411
$737$			6.27344e20i			0.195659i
$738$		0			0
$739$	3.98170e21			1.21685			0.608423	−	0.793613i	$-0.291803\pi$
$739$	3.98170e21			1.21685			0.608423	+	0.793613i	$0.291803\pi$
$740$	−3.10907e20	−	2.23114e20i	−0.0940572	−	0.0674978i
$741$		0			0
$742$			1.83290e20i			0.0543386i
$743$			4.07217e21i			1.19512i	0.801826	+	0.597558i	$0.203862\pi$
$743$			4.07217e21i			1.19512i	−0.801826	+	0.597558i	$0.796138\pi$
$744$		0			0
$745$	1.30336e21	−	1.81622e21i	0.374881	−	0.522391i
$746$	3.53212e21			1.00576
$747$		0			0
$748$		−	4.73051e20i		−	0.132022i
$749$	−1.58852e21			−0.438913
$750$		0			0
$751$	3.86005e21			1.04543			0.522713	−	0.852509i	$-0.324920\pi$
$751$	3.86005e21			1.04543			0.522713	+	0.852509i	$0.324920\pi$
$752$		−	6.20313e20i		−	0.166332i
$753$		0			0
$754$	2.31885e21			0.609520
$755$	1.95055e21	−	2.71806e21i	0.507638	−	0.707387i
$756$		0			0
$757$		−	2.80787e21i		−	0.716403i	−0.933644	−	0.358202i	$-0.883390\pi$
$757$		−	2.80787e21i		−	0.716403i	0.933644	−	0.358202i	$-0.116610\pi$
$758$			4.14416e21i			1.04693i
$759$		0			0
$760$	6.84106e20	+	4.90931e20i	0.169442	+	0.121596i
$761$	−2.34918e21			−0.576145			−0.288072	−	0.957609i	$-0.593014\pi$
$761$	−2.34918e21			−0.576145			−0.288072	+	0.957609i	$0.593014\pi$
$762$		0			0
$763$		−	1.90637e20i		−	0.0458431i
$764$	2.48735e21			0.592294
$765$		0			0
$766$	9.01922e20			0.210597
$767$		−	8.66615e21i		−	2.00383i
$768$		0			0
$769$	5.48498e21			1.24373			0.621867	−	0.783123i	$-0.286374\pi$
$769$	5.48498e21			1.24373			0.621867	+	0.783123i	$0.286374\pi$
$770$	3.02886e20	−	4.22068e20i	0.0680141	−	0.0947768i
$771$		0			0
$772$		−	2.36655e21i		−	0.521179i
$773$			7.45803e21i			1.62659i	0.581851	+	0.813295i	$0.302329\pi$
$773$			7.45803e21i			1.62659i	−0.581851	+	0.813295i	$0.697671\pi$
$774$		0			0
$775$	−1.02929e21	−	3.04585e21i	−0.220178	−	0.651548i
$776$	−1.22032e21			−0.258529
$777$		0			0
$778$			7.49308e20i			0.155709i
$779$	−2.85615e21			−0.587828
$780$		0			0
$781$	2.33659e21			0.471736
$782$			1.70995e21i			0.341927i
$783$		0			0
$784$	1.07615e21			0.211107
$785$	−7.74726e21	−	5.55962e21i	−1.50531	−	1.08025i
$786$		0			0
$787$		−	5.05701e21i		−	0.964013i	−0.876168	−	0.482007i	$-0.839908\pi$
$787$		−	5.05701e21i		−	0.964013i	0.876168	−	0.482007i	$-0.160092\pi$
$788$			2.77281e21i			0.523568i
$789$		0			0
$790$	−1.95101e21	−	1.40009e21i	−0.361457	−	0.259391i
$791$	1.03544e21			0.190021
$792$		0			0
$793$		−	6.50631e21i		−	1.17162i
$794$	−2.18338e21			−0.389471
$795$		0			0
$796$	1.83548e21			0.321294
$797$		−	9.99891e21i		−	1.73386i	−0.498426	−	0.866932i	$-0.666089\pi$
$797$		−	9.99891e21i		−	1.73386i	0.498426	−	0.866932i	$-0.333911\pi$
$798$		0			0
$799$	2.46807e21			0.420007
$800$	−9.93388e20	+	3.35697e20i	−0.167473	+	0.0565942i
$801$		0			0
$802$			2.70851e21i			0.448150i
$803$			3.46858e21i			0.568572i
$804$		0			0
$805$	−1.09485e21	+	1.52566e21i	−0.176151	+	0.245464i
$806$	4.49230e21			0.716070
$807$		0			0
$808$		−	3.88614e21i		−	0.608042i
$809$	−1.42599e21			−0.221056			−0.110528	−	0.993873i	$-0.535254\pi$
$809$	−1.42599e21			−0.221056			−0.110528	+	0.993873i	$0.535254\pi$
$810$		0			0
$811$	5.78120e21			0.879754			0.439877	−	0.898058i	$-0.355022\pi$
$811$	5.78120e21			0.879754			0.439877	+	0.898058i	$0.355022\pi$
$812$			7.65710e20i			0.115450i
$813$		0			0
$814$	−4.62649e20			−0.0684807
$815$	−5.04556e21	−	3.62082e21i	−0.739992	−	0.531037i
$816$		0			0
$817$		−	1.05357e21i		−	0.151705i
$818$			8.28500e21i			1.18207i
$819$		0			0
$820$	2.07370e21	−	2.88968e21i	0.290498	−	0.404805i
$821$	−2.77692e21			−0.385470			−0.192735	−	0.981251i	$-0.561736\pi$
$821$	−2.77692e21			−0.385470			−0.192735	+	0.981251i	$0.561736\pi$
$822$		0			0
$823$			1.24862e22i			1.70189i	0.525258	+	0.850943i	$0.323969\pi$
$823$			1.24862e22i			1.70189i	−0.525258	+	0.850943i	$0.676031\pi$
$824$	1.68414e21			0.227470
$825$		0			0
$826$	2.86165e21			0.379548
$827$		−	9.62865e21i		−	1.26553i	−0.774342	−	0.632767i	$-0.781919\pi$
$827$		−	9.62865e21i		−	1.26553i	0.774342	−	0.632767i	$-0.218081\pi$
$828$		0			0
$829$	3.86204e21			0.498492			0.249246	−	0.968440i	$-0.419817\pi$
$829$	3.86204e21			0.498492			0.249246	+	0.968440i	$0.419817\pi$
$830$	2.69803e21	−	3.75966e21i	0.345112	−	0.480909i
$831$		0			0
$832$		−	1.46514e21i		−	0.184057i
$833$			4.28174e21i			0.533068i
$834$		0			0
$835$	3.65696e21	+	2.62432e21i	0.447169	+	0.320899i
$836$	1.01799e21			0.123367
$837$		0			0
$838$		−	5.46758e21i		−	0.650826i
$839$	−2.06355e21			−0.243444			−0.121722	−	0.992564i	$-0.538842\pi$
$839$	−2.06355e21			−0.243444			−0.121722	+	0.992564i	$0.538842\pi$
$840$		0			0
$841$	−5.67193e21			−0.657296
$842$		−	1.97990e21i		−	0.227406i
$843$		0			0
$844$	1.00599e21			0.113508
$845$	6.08992e21	−	8.48622e21i	0.681062	−	0.949050i
$846$		0			0
$847$			2.96190e21i			0.325420i
$848$		−	4.47268e20i		−	0.0487079i
$849$		0			0
$850$	−1.33565e21	−	3.95244e21i	−0.142906	−	0.422886i
$851$	1.67235e21			0.177360
$852$		0			0
$853$		−	1.41542e22i		−	1.47492i	−0.675390	−	0.737461i	$-0.736025\pi$
$853$		−	1.41542e22i		−	1.47492i	0.675390	−	0.737461i	$-0.263975\pi$
$854$	2.14845e21			0.221918
$855$		0			0
$856$	3.87634e21			0.393431
$857$		−	1.25937e22i		−	1.26706i	−0.773720	−	0.633528i	$-0.781606\pi$
$857$		−	1.25937e22i		−	1.26706i	0.773720	−	0.633528i	$-0.218394\pi$
$858$		0			0
$859$	−8.84870e21			−0.874845			−0.437422	−	0.899256i	$-0.644108\pi$
$859$	−8.84870e21			−0.874845			−0.437422	+	0.899256i	$0.644108\pi$
$860$	1.06594e21	+	7.64943e20i	0.104470	+	0.0749706i
$861$		0			0
$862$			3.70909e21i			0.357243i
$863$			1.47249e22i			1.40595i	0.711214	+	0.702975i	$0.248146\pi$
$863$			1.47249e22i			1.40595i	−0.711214	+	0.702975i	$0.751854\pi$
$864$		0			0
$865$	4.29108e21	+	3.07939e21i	0.402667	+	0.288964i
$866$	2.40392e21			0.223633
$867$		0			0
$868$			1.48340e21i			0.135632i
$869$	−2.90323e21			−0.263168
$870$		0			0
$871$	−7.73076e21			−0.688789
$872$			4.65199e20i			0.0410927i
$873$		0			0
$874$	−3.67977e21			−0.319510
$875$	1.33898e21	−	4.38166e21i	0.115269	−	0.377206i
$876$		0			0
$877$			4.07982e21i			0.345258i	0.984987	+	0.172629i	$0.0552262\pi$
$877$			4.07982e21i			0.345258i	−0.984987	+	0.172629i	$0.944774\pi$
$878$			1.47479e22i			1.23743i
$879$		0			0
$880$	−7.39112e20	+	1.02994e21i	−0.0609663	+	0.0849557i
$881$	−1.67856e22			−1.37284			−0.686418	−	0.727208i	$-0.740818\pi$
$881$	−1.67856e22			−1.37284			−0.686418	+	0.727208i	$0.740818\pi$
$882$		0			0
$883$			9.14394e21i			0.735238i	0.929976	+	0.367619i	$0.119827\pi$
$883$			9.14394e21i			0.735238i	−0.929976	+	0.367619i	$0.880173\pi$
$884$	5.82941e21			0.464764
$885$		0			0
$886$	−7.32477e21			−0.574171
$887$			8.73083e21i			0.678623i	0.940674	+	0.339311i	$0.110194\pi$
$887$			8.73083e21i			0.678623i	−0.940674	+	0.339311i	$0.889806\pi$
$888$		0			0
$889$	6.75691e21			0.516398
$890$	−6.25973e21	−	4.49214e21i	−0.474385	−	0.340430i
$891$		0			0
$892$			5.96197e21i			0.444277i
$893$			5.31121e21i			0.392471i
$894$		0			0
$895$	−5.66346e21	+	7.89195e21i	−0.411537	+	0.573471i
$896$	4.83804e20			0.0348626
$897$		0			0
$898$			9.57482e21i			0.678513i
$899$	5.72908e21			0.402612
$900$		0			0
$901$	1.77957e21			0.122993
$902$		−	4.30002e21i		−	0.294728i
$903$		0			0
$904$	−2.52671e21			−0.170330
$905$	1.63556e22	−	2.27913e22i	1.09346	−	1.52372i
$906$		0			0
$907$		−	2.03388e22i		−	1.33743i	−0.743519	−	0.668715i	$-0.766845\pi$
$907$		−	2.03388e22i		−	1.33743i	0.743519	−	0.668715i	$-0.233155\pi$
$908$			1.08149e22i			0.705310i
$909$		0			0
$910$	5.20114e21	+	3.73247e21i	0.333648	+	0.239434i
$911$	−8.19631e21			−0.521472			−0.260736	−	0.965410i	$-0.583965\pi$
$911$	−8.19631e21			−0.521472			−0.260736	+	0.965410i	$0.583965\pi$
$912$		0			0
$913$		−	5.59461e21i		−	0.350138i
$914$	−9.10991e21			−0.565481
$915$		0			0
$916$	4.76691e20			0.0291086
$917$		−	5.52274e21i		−	0.334491i
$918$		0			0
$919$	−1.16604e22			−0.694777			−0.347389	−	0.937721i	$-0.612932\pi$
$919$	−1.16604e22			−0.694777			−0.347389	+	0.937721i	$0.612932\pi$
$920$	2.67169e21	−	3.72296e21i	0.157898	−	0.220029i
$921$		0			0
$922$		−	9.11060e20i		−	0.0529743i
$923$			2.87938e22i			1.66068i
$924$		0			0
$925$	−3.86552e21	+	1.30628e21i	−0.219354	+	0.0741265i
$926$	−9.47973e21			−0.533597
$927$		0			0
$928$		−	1.86851e21i		−	0.103487i
$929$	−3.18554e21			−0.175011			−0.0875056	−	0.996164i	$-0.527890\pi$
$929$	−3.18554e21			−0.175011			−0.0875056	+	0.996164i	$0.527890\pi$
$930$		0			0
$931$	−9.21418e21			−0.498120
$932$		−	2.40364e21i		−	0.128899i
$933$		0			0
$934$	−1.31280e22			−0.692781
$935$	−4.09788e21	−	2.94074e21i	−0.214522	−	0.153946i
$936$		0			0
$937$			1.91960e22i			0.988928i	0.869198	+	0.494464i	$0.164636\pi$
$937$			1.91960e22i			0.988928i	−0.869198	+	0.494464i	$0.835364\pi$
$938$		−	2.55278e21i		−	0.130464i
$939$		0			0
$940$	−5.37356e21	−	3.85619e21i	−0.270273	−	0.193955i
$941$	2.90690e22			1.45047			0.725233	−	0.688503i	$-0.241732\pi$
$941$	2.90690e22			1.45047			0.725233	+	0.688503i	$0.241732\pi$
$942$		0			0
$943$			1.55434e22i			0.763323i
$944$	−6.98309e21			−0.340218
$945$		0			0
$946$	1.58618e21			0.0760623
$947$			3.51817e21i			0.167376i	0.996492	+	0.0836878i	$0.0266698\pi$
$947$			3.51817e21i			0.167376i	−0.996492	+	0.0836878i	$0.973330\pi$
$948$		0			0
$949$	−4.27433e22			−2.00158
$950$	8.50554e21	−	2.87428e21i	0.395162	−	0.133537i
$951$		0			0
$952$			1.92493e21i			0.0880316i
$953$			4.14849e22i			1.88232i	0.337960	+	0.941161i	$0.390263\pi$
$953$			4.14849e22i			1.88232i	−0.337960	+	0.941161i	$0.609737\pi$
$954$		0			0
$955$	1.54627e22	−	2.15471e22i	0.690653	−	0.962416i
$956$	4.76125e21			0.211002
$957$		0			0
$958$			2.57623e22i			1.12394i
$959$	5.69520e21			0.246530
$960$		0			0
$961$	−1.23664e22			−0.527007
$962$		−	5.70122e21i		−	0.241076i
$963$		0			0
$964$	−6.27063e21			−0.261056
$965$	−2.05006e22	−	1.47118e22i	−0.846862	−	0.607729i
$966$		0			0
$967$			3.12652e22i			1.27163i	0.771840	+	0.635817i	$0.219337\pi$
$967$			3.12652e22i			1.27163i	−0.771840	+	0.635817i	$0.780663\pi$
$968$		−	7.22771e21i		−	0.291699i
$969$		0			0
$970$	−7.58613e21	+	1.05712e22i	−0.301462	+	0.420083i
$971$	2.79145e22			1.10074			0.550370	−	0.834921i	$-0.314487\pi$
$971$	2.79145e22			1.10074			0.550370	+	0.834921i	$0.314487\pi$
$972$		0			0
$973$			1.78673e22i			0.693767i
$974$	1.74942e22			0.674065
$975$		0			0
$976$	−5.24272e21			−0.198922
$977$			8.12156e21i			0.305795i	0.988242	+	0.152898i	$0.0488604\pi$
$977$			8.12156e21i			0.305795i	−0.988242	+	0.152898i	$0.951140\pi$
$978$		0			0
$979$	−9.31488e21			−0.345388
$980$	6.68993e21	−	9.32233e21i	0.246165	−	0.343028i
$981$		0			0
$982$		−	2.33351e22i		−	0.845617i
$983$			5.00817e22i			1.80106i	0.434794	+	0.900530i	$0.356821\pi$
$983$			5.00817e22i			1.80106i	−0.434794	+	0.900530i	$0.643179\pi$
$984$		0			0
$985$	2.40199e22	+	1.72372e22i	0.850744	+	0.610515i
$986$	7.43431e21			0.261315
$987$		0			0
$988$			1.25447e22i			0.434294i
$989$	−5.73361e21			−0.196995
$990$		0			0
$991$	−1.98490e22			−0.671717			−0.335859	−	0.941912i	$-0.609026\pi$
$991$	−1.98490e22			−0.671717			−0.335859	+	0.941912i	$0.609026\pi$
$992$		−	3.61985e21i		−	0.121577i
$993$		0			0
$994$	−9.50801e21			−0.314552
$995$	1.14103e22	−	1.59001e22i	0.374649	−	0.522069i
$996$		0			0
$997$			3.50665e22i			1.13417i	0.823659	+	0.567086i	$0.191929\pi$
$997$			3.50665e22i			1.13417i	−0.823659	+	0.567086i	$0.808071\pi$
$998$		−	8.07839e21i		−	0.259326i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.16.c.e.19.3	✓	16
3.2	odd	2	inner	90.16.c.e.19.14	yes	16
5.4	even	2	inner	90.16.c.e.19.11	yes	16
15.14	odd	2	inner	90.16.c.e.19.6	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.16.c.e.19.3	✓	16	1.1	even	1	trivial
90.16.c.e.19.6	yes	16	15.14	odd	2	inner
90.16.c.e.19.11	yes	16	5.4	even	2	inner
90.16.c.e.19.14	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	90.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-128.000i q^{2} -16384.0 q^{4} +(-101852. + 141929. i) q^{5} -859408. i q^{7} +2.09715e6i q^{8} +(1.81669e7 + 1.30370e7i) q^{10} +2.70335e7 q^{11} +3.33134e8i q^{13} -1.10004e8 q^{14} +2.68435e8 q^{16} +1.06804e9i q^{17} -2.29839e9 q^{19} +(1.66874e9 - 2.32536e9i) q^{20} -3.46029e9i q^{22} +1.25080e10i q^{23} +(-9.77005e9 - 2.89114e10i) q^{25} +4.26411e10 q^{26} +1.40805e10i q^{28} +5.43807e10 q^{29} +1.05351e11 q^{31} -3.43597e10i q^{32} +1.36709e11 q^{34} +(1.21975e11 + 8.75322e10i) q^{35} -1.33702e11i q^{37} +2.94193e11i q^{38} +(-2.97647e11 - 2.13598e11i) q^{40} +1.24268e12 q^{41} +4.58396e11i q^{43} -4.42917e11 q^{44} +1.60102e12 q^{46} -2.31085e12i q^{47} +4.00898e12 q^{49} +(-3.70066e12 + 1.25057e12i) q^{50} -5.45806e12i q^{52} -1.66620e12i q^{53} +(-2.75341e12 + 3.83683e12i) q^{55} +1.80231e12 q^{56} -6.96073e12i q^{58} -2.60140e13 q^{59} -1.95306e13 q^{61} -1.34850e13i q^{62} -4.39805e12 q^{64} +(-4.72813e13 - 3.39302e13i) q^{65} +2.32062e13i q^{67} -1.74987e13i q^{68} +(1.12041e13 - 1.56128e13i) q^{70} +8.64331e13 q^{71} +1.28307e14i q^{73} -1.71139e13 q^{74} +3.76567e13 q^{76} -2.32328e13i q^{77} -1.07394e14 q^{79} +(-2.73406e13 + 3.80988e13i) q^{80} -1.59063e14i q^{82} -2.06951e14i q^{83} +(-1.51585e14 - 1.08781e14i) q^{85} +5.86747e13 q^{86} +5.66933e13i q^{88} -3.44568e14 q^{89} +2.86298e14 q^{91} -2.04931e14i q^{92} -2.95788e14 q^{94} +(2.34094e14 - 3.26207e14i) q^{95} +5.81892e14i q^{97} -5.13149e14i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 262144 q^{4} - 49733632 q^{10} + 4294967296 q^{16} - 9028552704 q^{19} + 42419563632 q^{25} - 40724611904 q^{31} - 885646311424 q^{34} + 814835826688 q^{40} - 654599782400 q^{46} - 17251393932048 q^{49}+ \cdots - 909200639590400 q^{94}+O(q^{100}) \) 16 * q - 262144 * q^4 - 49733632 * q^10 + 4294967296 * q^16 - 9028552704 * q^19 + 42419563632 * q^25 - 40724611904 * q^31 - 885646311424 * q^34 + 814835826688 * q^40 - 654599782400 * q^46 - 17251393932048 * q^49 + 11333866801472 * q^55 + 92663079527072 * q^61 - 70368744177664 * q^64 - 33467474673664 * q^70 + 147923807502336 * q^76 + 543959857901376 * q^79 - 1590761422616992 * q^85 + 2706439057736832 * q^91 - 909200639590400 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

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Database

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